c2 Test of Independence
& Goodness of Fit

But, you tell your client that's not good enough evidence. You make up the following chart:

 

It's just chance - the office could be either 5 males versus 5 females but just the change of one person would make it 6 to 4. It could have just as easily been 4 males or 6 females.

Intuitively, you can see that it would be hard to convince someone that this 60 - 40 split is discrimination. It's too easy to be just luck.

••• What if the company only had 5 managers in the office? •••

It would have to be 60-40 (3 vs 2). The 60-40 or 40-60 means nothing in this case.

Like this:

 

If you understand our pictures - you understand Chi-Square's purpose.

Again - you have a set of proportions - you think should be true (Expected) and you test them against a set that you have observed (Observed).

You see if the differences in O Vs E are big enough not to be pure luck!

In case, the differences could easily be chance as O - E is small {this sentence confuses me – are some words missing?}

Your client won't give up. She says:

OK - If there was no discrimination, you should get the following picture with 50 men and 50 women.

The Ideal or Expected Office Distribution of Managers